Ramsey families which exclude a graph

For graphsA andB the relationA(B) _r ¹ means that for everyr-coloring of the vertices ofA there is a monochromatic copy ofB inA. Forb (G) is the family of graphs which do not embedG. A familyof graphs is Ramsey if for all graphsBthere is a graphAsuch thatA(B) _r ¹ . The only graphsG for which it is not known whether Forb (G) is Ramsey are graphs which have a cutpoint adjacent to every other vertex except one. In this paper we prove for a large subclass of those graphsG, that Forb (G) does not have the Ramsey property.This research has been supported in part by NSERC grant 69-1325.     

Interspike interval embedding of chaotic signals

According to a theorem of Takens [Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898], dynamical state information can be reproduced from a time series of amplitude measurements. In this paper we investigate whether the same information can be reproduced from interspike interval (ISI) measurements. Assuming an integrate-and-fire model coupling the dynamical system to the spike train, there is a one-to-one correspondence between the system states and interspike interval vectors of sufficiently large dimension. The correspondence implies in particular that a data series of interspike intervals, formed in this manner, can be forecast from past history. This capability is demonstrated using a nonlinear prediction algorithm, and is found to be robust to noise. A set of interspike intervals measured from a simple neuronal circuit is studied for deterministic structure using a prediction error statistic. (c) 1995 American Institute of Physics.     

Zur Reaktion von Pyridin-2,6-dicarbonsäure mit Aluminium(III) in wäßriger Lösung

Contrary to the informations in the literature our results of equilibrium and kinetic measurements indicate that Al(III) and Pyridine-2,6-dicarboxylic Acid in the range ofpH=(3...5) only formed the complexes AlHL ²⁺ (log=7.44±0.2) and AlL ⁺ (log=11.37±0.06).     

Formation of Ad-Layers and Clusters on Condensation of Metal Vapors on Solid Surfaces

Synthesis of organometallic materials can be accomplished in many cases by cocondensation of metal atoms and organic molecules at low temperatures. The reaction kinetics is determined by the competition between metal cluster growth and formation of the organometallic compound. Interesting compounds may contain one or more metal atoms; the latter type could be obtained by reaction between a cluster containing the desired number of metal atoms and an organic molecule. A precise knowledge of the events occurring on condensation of metal atoms and cluster formation can therefore be of value in the control of chemical synthesis. These phenomena have been investigated in connection with the study of the growth of thin metallic films, both experimentally and theoretically. Direct observation of the formation of very small clusters is difficult. The good agreement between experimental results and recent calculations for the development of large clusters, however, allows reliable theoretical conclusions for the first stages of adsorption and cluster formation. The present contribution describes experimental work on film growth and relevant theoretical concepts, and an attempt is made to develop applications to organometallic synthesis.     

Synthesis and acid-base properties of (1H-benzimidazol-2-yl-methyl)phosphonate (Bimp2-). Evidence for intramolecular hydrogen-bond formation in aqueous solution between (N-1)H and the phosphonate group

The synthesis of (1H-benzimidazol-2-yl-methyl)phosphonic acid, H2(Bimp)+/-, is described: 2-chloromethylbenzimidazole was reacted with ethylchloroformate to give 1-carboethoxy-2-chloromethylbenzimidazole which was treated with trimethyl phosphite and after hydrolysis with aqueous HBr H2(Bimp)+/- was obtained. In H2(Bimp)+/- one proton is at the N-3 site and the other at the phosphonate group; both acidity constants were determined in aqueous solution by potentiometric pH titrations (25 degrees C; I = 0.1 M, NaNO3) and this furnished the pKa values of 5.37 +/- 0.02 and 7.41 +/- 0.02, respectively. The acidity constant for the release of the primary proton from the P(O)(OH)2 group of H3(Bimp)+ was estimated: pKa = 1.5 +/- 0.2. Moreover, Bimp2- can be further deprotonated at its neutral (N-1/N-3)H site to give the benzimidazolate residue, but this reaction occurs only in strongly alkaline solution (KOH); application of the H_ scale developed by G. Yagil (J. Phys. Chem., 1967, 71, 1034) together with UV spectrophotometric measurements gave pKa = 14.65 +/- 0.12. Comparisons with acidity constants taken from the literature show that this latter pKa value is far too large and this allows the conclusion that an intramolecular hydrogen bond is formed between the (N-1/N-3)H site and the phosphonate group of Bimp2-; the formation degree of this hydrogen-bonded isomer is estimated to be 98 +/- 2%. The general relevance of this and the other results are shortly discussed and the species distribution for the Bimp system in dependence on pH is provided.     

Determination of titanium by adsorption voltammetry with 4-(2-pyridylazo) resorcinol

Summary Titanium (IV) forms a complex with 4-(2-pyridylazo) resorcinol (PAR) in weakly acidic solutions. This complex can be used to determine titanium by adsorption voltammetry at a stationary Hg-electrode. The experimental conditions for the determination are described. The current-concentration curve is linear from 0.15–4.8 ng/g. Ti at a deposition time of 3 min, the detection limit lies at 0.1 ng/g. The influence of foreign ions was investigated. The determination can be carried out in the presence of a 1000-fold excess of iron by the standard addition method, albeit with decreased sensitivity.     

A simple and efficient one step synthesis of 1,3,4-oxadiazoles utilizing polymer-supported reagents and microwave heating

1,3,4-Oxadiazoles can be rapidly and efficiently synthesized from a variety of carboxylic acids and acid hydrazides in one simple step. The use of commercially available PS-PPh₃ resin combined with microwave heating delivered the product 1,3,4-oxadiazoles in high yields and purities.